Class 8 Maths

Factorisation

Exercise 14.2

Question 1: Find the common factors of the given terms.

(i) 12x, 36

Answer: `12x=2xx2xx3xx\x`

`36=2xx2xx3xx3`

Here, common factor `= 2xx3=6`

(ii) 2y, 22xy

Answer: `2y=2xx\y`

`22y=2xx11xx\y`

Common factor = 2

(iii) 14 pq, 28 p2q2

Answer: `14pq=2xx7xx\p\xx\q`

`28p^2q^2=2xx2xx7xx\p\xx\p\xx\q\xx\q`

Common factor `=2xx7xx\p\xx\q`


(iv) 2x, 3x², 4

Answer: `2x=2xx\x`

`3x^2=3xx\x\xx\x`

`4=2xx2`

Common factor = 1

There is no common factor other than unity, so common factor= 1

(v) 6 abc, 24ab², 12 a²b

Answer: `6abc=2xx3xx\a\xx\b\xx\c`

`24ab^2=2xx2xx2xx3xx\a\xx\b\xx\b`

`12a^2b=2xx2xx3xx\a\xx\a\xx\b`

(vi) 16 x³, – 4x², 32x

Answer: `16x^3=2xx2xx2xx2xx\a\xx\a\xx\a`

`-4x^2=-2xx2xx\x\xx\x`

`32x=2xx2xx2xx2xx2xx\x`

Common factor `=2x`

(vii) 10 pq, 20qr, 30rp

Answer: `10pq=2xx5xx\p\xx\q`

`20qr=2xx2xx4xx\q\xx\r`

`30rp=2xx3xx5xx\r\xx\p`

Common factor `=2xx5=10`

(viii) 3x² y³, 10x³ y²,6 x² y²z

Answer: `3x^2y^3=3xx\x\xx\x\xx\y\xx\y\xx\y`

`10x^3y^2=2xx5xx\x\xx\x\xx\x\xx\y\xx\y`

`x^2y^2z=x\xx\x\xx\y\xxy\xx\z`

Common factor`=x^2y^2`


Question 2: Factorise the following expressions.

(i) 7x – 42

Answer: `7x-42`

`=7xx\x-7xx6=7(x-6)`

(ii) 6p – 12q

Answer: `6p-12q`

`=6xx\p-6xx2q=6(p-2q)`

(iii) 7a² + 14a

Answer: `7a^2+14a`

`=7xx\a\xx\a+7xx2xx\a=7a(a+2)`

(iv) – 16 z + 20 z³

Answer: `-16z+20z^3`

`=4xx4xx\z+4xx5xx\z\xx\z\xx\z`

`=4z(-4+5z\xx\z)=4z(5z^2-4)`

(v) 20 l² m + 30 a l m

Answer: `20l^2m+30alm`

`=2xx2xx5xx\l\xx\l\xx\m+2xx3xx5xx\a\xx\l\xx\m`

`=2lm(10l+15a)`

(vi) 5 x² y – 15 xy²

Answer: `5x^2y-15xy^2`

`=5xx\x\xx\x\xx\y-3xx5xx\x\xx\y\xx\y`

`=5x(xy-3y^2)`

(vii) 10 a² – 15 b² + 20 c²

Answer: `10a^2-15b^2+20c^2`

`=2xx5xx\a\xx\a-3xx5xx\b\xx\b+4xx5xx\c\xx\c`

`=5(2a^2-3b^2+4c^2)`


(viii) – 4 a² + 4 ab – 4 ca

Answer: `-4a^2+4ab-4ca`

`=-4xx\a\xx\a+4xx\a\xx\b-4xx\c\xx\a`

`=-4a(a-b+c)`

(ix) x² y z + x y²z + x y z²

Answer: `x^2yz+xy^2z+xyz^2`

`=x\xx\x\xx\y\xx\z+x\xx\y\xx\y\xx\z+x\xx\y\xx\z\xx\z`

`=xyz(x+y+z)`

(x) a x² y + b x y² + c x y z²

Answer: `ax^yz+bxy^2z+cxyz^2`

`=a\xx\x\xx\x\xx\y\xx\z+b\xx\x\xx\y\xx\y\xx\z+c\xx\x\xx\y\xx\z\xx\z`

`=xyz(ax+by+cz)`

Question 3: Factorise.

(i) x² + x y + 8x + 8y

Answer: `x^2+xy+8x+8y`

`=x\xx\x+x\xx\y+8xx\x+8xx\y`

`=x(x+y)+8(x+y)`

`=(x+8)(x+y)`

(ii) 15 xy – 6x + 5y – 2

Answer: `15xy-6x+5y-2`

`=3xx5xx\x\xx\y-2xx3xx\x+5xx\y-2`

`=3x(5y-2)+1(5y-2)`

`=(3x+1)(5y-2)`

(iii) ax + bx – ay – by

Answer: `ax+bx-ay-by`

`=x(a+b)-y(a+b)`

`=(x-y)(a+b)`

(iv) 15 pq + 15 + 9q + 25p

Answer: `15pq+15+9q+25p`

`=5xx3xx\pq+5xx3+3xx3q+5xx5p`

`=5xx3pq+3xx3q+5xx5p+5xx3`

`=3q(5p+3)+5(5p+3)`

`=(3q+5)(5p+3)`

(v) z – 7 + 7 x y – x y z

Answer: `z-7+7xy-xyz`

`=z-xyz-7+7xy`

`=z(1-xy)-7(1-xy)`

`=(z-7)(1-xy)`


Ex 14.1

Ex 14.2

Ex 14.3

Ex 14.4